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A224138 Number of 7 X n 0..1 arrays with rows nondecreasing and antidiagonals unimodal. 1
128, 2187, 9688, 25047, 52581, 101412, 186348, 329167, 561329, 927323, 1488515, 2327716, 3554534, 5311574, 7781550, 11195373, 15841279, 22075061, 30331469, 41136842, 55123036, 73042712, 95786048, 124398939, 160102749, 204315679 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Row 7 of A224133.
LINKS
FORMULA
Empirical: a(n) = (4/315)*n^7 + (1/5)*n^6 + (112/45)*n^5 + (461/24)*n^4 + (19267/180)*n^3 + (50171/120)*n^2 + (463243/420)*n - 511 for n>5.
Conjectures from Colin Barker, Aug 27 2018: (Start)
G.f.: x*(128 + 1163*x - 4224*x^2 + 1611*x^3 + 9957*x^4 - 14526*x^5 + 3960*x^6 + 4357*x^7 - 1401*x^8 - 1818*x^9 + 659*x^10 + 353*x^11 - 155*x^12) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>13.
(End)
EXAMPLE
Some solutions for n=3:
..0..0..1....1..1..1....0..1..1....0..0..0....1..1..1....0..0..0....0..1..1
..0..1..1....0..0..1....1..1..1....1..1..1....1..1..1....0..0..0....0..0..1
..0..0..1....0..0..1....1..1..1....1..1..1....0..0..1....0..1..1....0..1..1
..0..0..0....0..0..1....0..0..0....0..1..1....0..0..0....1..1..1....0..0..0
..0..1..1....0..0..1....0..1..1....0..0..0....0..0..0....0..0..1....0..1..1
..0..0..0....0..1..1....0..0..1....0..0..1....0..0..0....0..1..1....0..0..0
..0..0..1....0..0..1....0..0..0....0..0..0....1..1..1....0..0..0....0..0..0
CROSSREFS
Cf. A224133.
Sequence in context: A321831 A351195 A223954 * A331198 A250365 A017678
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 31 2013
STATUS
approved

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Last modified February 23 01:12 EST 2024. Contains 370265 sequences. (Running on oeis4.)